An encoder includes a periodic-combined-envelope generating part and a variable-length coding part. The periodic-combined-envelope generating part generates a periodic combined envelope sequence which is a frequency-domain sequence based on a spectral envelope sequence which is a frequency-domain sequence corresponding to a linear predictive coefficient code obtained from an input audio signal and on a frequency-domain period. The variable-length coding part encodes a frequency-domain sequence derived from the input audio signal. A decoder includes a periodic-combined-envelope generating part and a variable-length decoding part. The periodic-combined-envelope generating part generates a periodic combined envelope sequence which is a frequency-domain sequence based on a spectral envelope sequence which is a frequency-domain sequence corresponding to a linear predictive coefficient code and on a frequency-domain period. The variable-length decoding part decodes a variable-length code to obtain a frequency-domain sequence.